To summarize the linked thread: Some browsers, when you load an "https" page will complain if any of the elements on that page load over "http". For example, the story above loads some Twitter-y stuff from http://platform.twitter.com.
The technically correct fix is for the site owner to modify the page to load all these resources over https when the page is accessed over https. Until they do that, as a workaround, you could install an extension like the one mentioned by fl3tch[1] to do it in your browser.
N.B. That only works if the resource is available over https, many are not. In that case there is no fix.